Last active
October 3, 2018 01:12
-
-
Save hellman/0fd746dfe80c2ce8e75248b337cbd7a5 to your computer and use it in GitHub Desktop.
HXP CTF 2017 - flea (Crypto 150), CodeGate 2018 Quals - RsaBaby
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# FLEA | |
''' | |
n, l mod 2^t depend only on p,q mod 2^t. | |
So we can recover p,q bit-by-bit from LSB. | |
Given p mod 2^t, q mod 2^t = (n / p) mod 2^t is unique. | |
Ideally, l would give 1/2^t filter, | |
but here it gives a bit less and we get up to 2000 candidates in the end. | |
''' | |
from libnum import * | |
n = 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 | |
l = 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 | |
ct = 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 | |
sols = {(0, 0)} | |
for m in xrange(1111): | |
print m, "bits", len(sols), "candidates" | |
sols2 = set() | |
mask = (2 << m) - 1 | |
for x, y in sols: | |
if x * y == n: | |
d = invmod(65537, (x-1)*(y-1)) | |
print `n2s(pow(ct, d, n))` | |
#'hxp{T0t4LLy_r3aL1st1c_Le4kag3}\n' | |
quit() | |
for bx in xrange(2): | |
for by in xrange(2): | |
xx = x + (bx << m) | |
yy = y + (by << m) | |
if (xx * yy) & mask != n & mask: | |
continue | |
ll = (xx ^ yy) * (xx + yy) | |
if ll & mask != l & mask: | |
continue | |
sols2.add((xx, yy)) | |
sols = sols2 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# FLEA | |
#!/usr/bin/env python3 | |
import random, gmpy2 | |
random = random.SystemRandom() | |
bits = 2048 | |
p = gmpy2.next_prime(random.randrange(1 << bits // 2)) | |
q = gmpy2.next_prime(random.randrange(1 << bits // 2)) | |
n = p * q | |
l = (p ^ q) * (p + q) | |
flag = open('flag.txt', 'rb').read() | |
m = int.from_bytes(flag, 'big') | |
with open('data.txt', 'w') as f: | |
f.write('{:#x}\n'.format(n)) | |
f.write('{:#x}\n'.format(l)) | |
f.write('{:#x}\n'.format(pow(m, 65537, n))) | |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# FLEA | |
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 | |
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 | |
0xdbe279d9beb56937b6cbf8d9fbcec7a687685b732aad5b4bb99514b8872b8a9c2e0794a2f0e7a44fd969091dc0ddb7e783cd09504cbdd4b492919c0b37503dae1368961ccfa2b2eeba88491cfa9501073ebd5116c1dfd4a9bbbf47d00fafef71ff73038885a3bb72b524b7ca73e33b8cdda2728d0f4c5e3fb57576aa138047e4579c4ddc29c302ace4ff2abeccf13f77a0760f26509f4d5c12bfd4064da6ba6ff2474ce99db1dbeb506447b6fed882404aa8da8809acd7c80dd6d3ce0b5b6cce7a962e62ca1670dc86dec97f29a222391c4cbcbf60c71eead6a66cd75cb301fcb469eb103593d73cc310c82539f5cffaf311d122e2bf8e18e849fd486cbde42 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# RSABaby | |
from libnum import * | |
ct = 380838525806255337893946743050327173947433371586247814759050430578204300094635270877953690129762202769875996939276197842147224857220372679703619497806927398399795108952962442891905146440202908075035070979097412854358636621348531277713225298087614167276769631514565642627640343771883615641654535423058064397195504442204533423747451626752470200734177912209703945585196661670059908372263823148356525332391696830864610833871912286943309315368473809329884078356658600058695228563250424729883958206468130236010169302227516477051342268478958591705205358855157076547042386496593253499052139707216013118968009859098636706611794339780312391554420587540660796607687910531233690474314728367495027785278881971814489961127141923005420385579115964806930701533734013794866357390109761177291603859980361697959155126598284421792362843501361967548503757576918138895493498276658301936707818035503138088925361983300854592909022681075014994189523262500924039153521343614460622246152945716505290603455309333333560506091410274263241508522602811994582040578653226240563907254131889033343189265841619698442130035569880428826546382882121430886993470180883869383405219173399698928360778092640513571913940390199302310817294277155376000921294944591121246587133744 | |
n = 523639805914061918270627443134741619704989339108811345591765650823383811679404400743730300288077320843234806116907796484315512386749183735427076044515394957782722144465236043561036957495670530886847413432636828661793513741180618385135095922719611444315861194066682307139969523206842728092440966461922557111209480112023032164065707216752568624317883094770784553451376502893748762652573604180632157059219119741129827017117558208565054860250853978397405747507844727903363351081745897472675235414693294079400158465019978970101063161094836772073302365997371679643083941089269169502839517043186914783290465318781726781533226599462066259256698885200843104424722505593942510854302401488139137362276492532699951880474157691347473741517183512613811731637427562990396497067805682564174185792379491573312640862381843195615293946630128509982267460922475624107750277459002662884836031305873522960659017891138316482378312004790485681371129328860344989214941450460756203906709954285455206483931555441550631622907560476932030275168094874500348941952385811045752980245084909805234648503736291123092594689494187215718382724496356220857628352007757197464098872772987476828030721472777531411032286344430474215475330008833588291692767417022829531866323051 | |
h = 200972731730097636976827049698214756107439330058946586294810837394189769656758467301378455256704981506024979360358854939307759891385801491668590432728409172325924823845795802068569504027458509726942683684845099685005724309372842055251251103232234279320256975662933177657993600463290652464246399357992101963313348397652939723188131041888535203383479379782750484175239116419074864386243581748425119257869351582631464696880797553969260415636591522791709442079709586828716914705946883433533874750682958642851920347897328709815665287336267018234850211541263570668304013958387590188226346947851729783080697306777656948546082 | |
g = 14511485561279877242490049924164262671564856980418706493772866848857612385453104346586350276227873984815502106112389832011566814347565705873657427101510533972939335373118027470906354834216983842099812965592939768854241417529908124711818216182341332507918374220901579987851767888710421089266081280013256600425746557269742268670300714949183260246617797156425767983027415373581836147225552931559016487193903056680274018867169067069164417868649729813464306199388375773268972224468436723728788928618254041886532217172217283880677562744928063668302190530092708676086756514664006766909499651097644447881334032649057611965077951245778537347658519214651268439995915614667939336569800565797702566887133370244643122543689011224353239395653153094885449557256699923700742653930928887024447374907536229536501931493386170594869542262576409686250950887746501725676758035668270309685358291271363775138099327895323451901829587908987436831617628346535627562925010698445652286450107659802164994355539623617745529876829000553355956755914526849056343372137493951531663650121127924626353148067965144997177441402726593083629261964699315644045714647617156724816370270635144953182744245498998992807987174252376199074131496163299914588620694929584594866873400406185502626180264465104468365933575409921644759774899908018217623256295871823903858740112075223018089096313796599554636163186830200265892525403238639070366999401808068998639590975305617369688731214141047568939908240058088089504343104889824160334560324387496383256518400827927341943755279126157377196722373876343583757261084975726106468397487366825775319965557539853162973895788663508023419482720093445137085452233528426725965549266605359644884153719762909553953900709890192728260024241748671796401590112629479273363064208874240854298225057415248756216847693518038319188675206377870041466557414694779134628404260587970 | |
e = 65537 | |
sols = {(0, 0, 0)} | |
for m in xrange(11111): | |
print m, "bits", len(sols), "candidates" | |
sols2 = set() | |
mask = (2 << m) - 1 | |
for x, y, d in sols: | |
if x * y == n: | |
d = invmod(65537, (x-1)*(y-1)) | |
print `n2s(pow(ct, d, n))` | |
quit() | |
for bx in xrange(2): | |
for by in xrange(2): | |
xx = x + (bx << m) | |
yy = y + (by << m) | |
if (xx * yy) & mask != n & mask: continue | |
for bd in xrange(2): | |
dd = d + (bd << m) | |
# h = (d+p)^(d-p) | |
# g = d*(p-0xdeadbeef) | |
if h & mask != ((d + xx) ^ (d - xx)) & mask: continue | |
if g & mask != (d*(xx-0xdeadbeef)) & mask: continue | |
sols2.add((xx, yy, dd)) | |
sols = sols2 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# RSABaby | |
def GenerateKeys(p, q): | |
e = 65537 | |
n = p * q | |
pi_n = (p-1)*(q-1) | |
d = mulinv(e, pi_n) | |
h = (d+p)^(d-p) | |
g = d*(p-0xdeadbeef) | |
return [e, n, h, g] |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# RSABaby | |
[*] Encrypted Data : 380838525806255337893946743050327173947433371586247814759050430578204300094635270877953690129762202769875996939276197842147224857220372679703619497806927398399795108952962442891905146440202908075035070979097412854358636621348531277713225298087614167276769631514565642627640343771883615641654535423058064397195504442204533423747451626752470200734177912209703945585196661670059908372263823148356525332391696830864610833871912286943309315368473809329884078356658600058695228563250424729883958206468130236010169302227516477051342268478958591705205358855157076547042386496593253499052139707216013118968009859098636706611794339780312391554420587540660796607687910531233690474314728367495027785278881971814489961127141923005420385579115964806930701533734013794866357390109761177291603859980361697959155126598284421792362843501361967548503757576918138895493498276658301936707818035503138088925361983300854592909022681075014994189523262500924039153521343614460622246152945716505290603455309333333560506091410274263241508522602811994582040578653226240563907254131889033343189265841619698442130035569880428826546382882121430886993470180883869383405219173399698928360778092640513571913940390199302310817294277155376000921294944591121246587133744 | |
[*] N : 523639805914061918270627443134741619704989339108811345591765650823383811679404400743730300288077320843234806116907796484315512386749183735427076044515394957782722144465236043561036957495670530886847413432636828661793513741180618385135095922719611444315861194066682307139969523206842728092440966461922557111209480112023032164065707216752568624317883094770784553451376502893748762652573604180632157059219119741129827017117558208565054860250853978397405747507844727903363351081745897472675235414693294079400158465019978970101063161094836772073302365997371679643083941089269169502839517043186914783290465318781726781533226599462066259256698885200843104424722505593942510854302401488139137362276492532699951880474157691347473741517183512613811731637427562990396497067805682564174185792379491573312640862381843195615293946630128509982267460922475624107750277459002662884836031305873522960659017891138316482378312004790485681371129328860344989214941450460756203906709954285455206483931555441550631622907560476932030275168094874500348941952385811045752980245084909805234648503736291123092594689494187215718382724496356220857628352007757197464098872772987476828030721472777531411032286344430474215475330008833588291692767417022829531866323051 | |
[*] h : 200972731730097636976827049698214756107439330058946586294810837394189769656758467301378455256704981506024979360358854939307759891385801491668590432728409172325924823845795802068569504027458509726942683684845099685005724309372842055251251103232234279320256975662933177657993600463290652464246399357992101963313348397652939723188131041888535203383479379782750484175239116419074864386243581748425119257869351582631464696880797553969260415636591522791709442079709586828716914705946883433533874750682958642851920347897328709815665287336267018234850211541263570668304013958387590188226346947851729783080697306777656948546082 | |
[*] g : 14511485561279877242490049924164262671564856980418706493772866848857612385453104346586350276227873984815502106112389832011566814347565705873657427101510533972939335373118027470906354834216983842099812965592939768854241417529908124711818216182341332507918374220901579987851767888710421089266081280013256600425746557269742268670300714949183260246617797156425767983027415373581836147225552931559016487193903056680274018867169067069164417868649729813464306199388375773268972224468436723728788928618254041886532217172217283880677562744928063668302190530092708676086756514664006766909499651097644447881334032649057611965077951245778537347658519214651268439995915614667939336569800565797702566887133370244643122543689011224353239395653153094885449557256699923700742653930928887024447374907536229536501931493386170594869542262576409686250950887746501725676758035668270309685358291271363775138099327895323451901829587908987436831617628346535627562925010698445652286450107659802164994355539623617745529876829000553355956755914526849056343372137493951531663650121127924626353148067965144997177441402726593083629261964699315644045714647617156724816370270635144953182744245498998992807987174252376199074131496163299914588620694929584594866873400406185502626180264465104468365933575409921644759774899908018217623256295871823903858740112075223018089096313796599554636163186830200265892525403238639070366999401808068998639590975305617369688731214141047568939908240058088089504343104889824160334560324387496383256518400827927341943755279126157377196722373876343583757261084975726106468397487366825775319965557539853162973895788663508023419482720093445137085452233528426725965549266605359644884153719762909553953900709890192728260024241748671796401590112629479273363064208874240854298225057415248756216847693518038319188675206377870041466557414694779134628404260587970 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
👍
didn't come up with the idea to recover bit-by-bit!